IEEE JOURNAL OF EMERGING AND SELECTED TOPIC IN POWER

2168-6777 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JESTPE.2017.2735964, IEEE Journal

of Emerging and Selected Topics in Power Electronics

IEEE JOURNAL OF EMERGING AND SELECTED TOPIC IN POWER ELECTRONICS, MARCH 2017 1

Analysis, Design and Maximum Power Efficiency

Tracking for Undersea Wireless Power TransferTaofeek Orekan, Member, IEEE, Peng Zhang, Senior Member, IEEE, and Cyuansi Shih

Abstract—In this paper, a detailed analysis that yields in-depthinsight into the design of undersea wireless power transfer systemis presented. Based on the analytical results, a methodology foroptimized coil design to increase the power transfer efficiency ispresented. Owing to the constant motion experienced by underseawireless power transfer system, a necessary feature is the abilityto operate at a multitude of distances without the need for manualtuning to maintain high efficiency. To address this, we propose anovel Maximum Power Efficiency Tracking (MPET) method thatuses k-Nearest Neighbors (kNN) to estimate the system’s couplingcoefficient and tracks the peak efficiency (> 85%) through anadaptive converter control. Simulation and experimental testresults validate the effectiveness and robustness of MPET inachieving maximum wireless power transfer efficiency under adynamic and uncertain undersea environment.

Index Terms—Maximum power efficiency tracking (MPET),undersea wireless power transfer, k-nearest neighbor, DC-DCconverter, smart ocean system.

I. INTRODUCTION

W Ireless power transfer (WPT) has been revitalized

largely because of the fast expanding market of mobile

devices and electric vehicles [1], [2], [3], [4]. Recently, WPT is

found to be critically needed in distributed ocean systems that

consume excessive power [5], such as an autonomous under-

water vehicle (AUV), underwater sensing nodes, ocean moni-

toring devices, etc. The traditional way of recharging/replacing

these devices manually is time-consuming, resulting in limited

operation range and disrupted services.

One potential solution is to build underwater docking sta-

tion with electrical connectors [6], [7], [8], which, however,

suffers from high maintenance costs and limits to near shore

applications. Here, WPT is investigated as a potent solution

to recharge distributed ocean systems. A design concept of

WPT for ocean systems application is shown in Fig. 1. The

ongoing research of WPT systems is mainly focused on land-

based applications [9]. Frequency tuning that automatically

adjusts the operating frequency to maximize system efficiency

has been developed in [10], [11], [12], [13]. Other methods

such as impedance matching [14], [15], [16], intermediate

field repeaters [17] [18], and the use of meta-materials [19],

[20] to achieve higher power transfer efficiency for WPT

in air have also been investigated. Nevertheless, transferring

power wirelessly in a marine environment, where seawater is a

conducting medium, is still an open and challenging problem.

T. Orekan, P. Zhang are with the Department of Electrical and ComputerEngineering, University of Connecticut, Storrs, CT 06269, USA (e-mail:[email protected], [email protected])

C. Shih is with the Department of Mechanical Engineering, University ofConnecticut, Storrs, CT 06269, USA.

Ocean surface

Ocean floor

Wave

energy

converter

Moored

sensor

Sensor package

AUV

Wireless power

transfer to sensorsSecondary

coil

Contains

primary

coil

Wireless

power

transmission

Fig. 1. A design concept of wireless power transfer for ocean systemsapplication.

Several questions to be addressed are: What is the effect

of the highly conductive seawater on a WPT system’s elec-

trical parameters? What is the effect of seawater on its coil

radiation resistance and the losses incurred? If the losses are

highly frequency-dependent, then how to choose an operating

frequency range in which high efficiency power transfer is

possible? Besides, the dynamic nature of the ocean makes the

WPT system constantly in motion and leads to time-varying

coupling coefficient, which necessitates an optimized design

strategy to overcome such expected variability. Furthermore,

control methods used in the WPT system in air, such as

impedance matching [14], [16], require information from the

transmitter through communication to keep track of changes in

the system parameters, making them inviable for an undersea

WPT (UWPT) system. Rather, a control method that uses

information from only the transmitting or receiving side of

the system without a communication network is essential.

To address the above challenges, this paper presents a

comprehensive UWPT efficiency analysis and MPET control

for maximizing undersea power transfer efficiency in real-time.

The major contributions of this paper are three-fold.

1) The electrical properties of the UWPT coils sub-

merged in seawater are quantified. The frequency-

dependent characteristics of the coil impedance, the

self-inductances, mutual inductance, the effects of coil

shapes are analyzed and compared to those of WPT in

the air.





2) A methodology for optimized coil design to increase

power transfer efficiency is developed based on the

above analytical results.

3) A novel Maximum Power Efficiency Tracking (MPET)

control method is introduced for achieving a maximum

power efficiency without communication or feedback

from the transmitting side of the UWPT system. In

particular, a k-nearest-neighbors-based machine learning

approach is devised for a real-time estimation of the

coupling coefficient from the receiving side, and the

output voltage is directly controlled using a DC-DC

converter to track maximum power transfer efficiency.

The estimated coupling coefficient is compared to refer-

ence coupling coefficient, and the robustness of the MPET

controller is verified through simulations. Also, this work

constitutes an extended version of our conference paper in [5].

II. UWPT SYSTEM OVERVIEW

Fig. 2 depicts the equivalent circuit model of the series-

series (SS) inductive UWPT system. An SS topology is

adopted in this paper because it allows high power to flow

on the receiver side, and it is proven to be more efficient

than series-parallel and parallel-series circuit topologies [21],

[22]. The circuit model includes the 3D geometry of the

coils in a marine environment. In the primary side of the

system is a transmitter coil (Tx) and in the secondary side

is the receiver coil (Rx), which are magnetically coupled by a

coupling coefficient kp/s. Here Lp, Ls, Cp, Cs, Rp, and Rs

represent inductances, series-resonance capacitors, and internal

resistances of the primary and secondary circuit, respectively,

and the primary and secondary side voltages are defined as Vp

and Vs, respectively. The load resistance is RL. The secondary

voltage to primary voltage ratio is derived as:

Vs

Vp=

(ω0Lm)RL

(RL +Rs)(RpRs + (ω0Lm)2)(1)

Assuming the transmitting frequency is the same as the

resonance frequency of the UWPT, the power transmitting

efficiency (ηpt) can be written as:

ηpt =(ω0Lm)2RL

(RL +Rs)(RLRp +RpRs + (ω0Lm)2)(2)

where

ω0 =1

√

LpCp

=1√LsCs

(3)

corresponds to the resonance frequency, and Lm is the mutual

inductance which is directly related to the distance between

the coils. Lm is responsible for how much power is transferred

and its normalized form, coupling coefficient kp/s (defined

below), is used to indicate whether the UWPT is over-coupled,

critically coupled or under-coupled.

kp/s =Lm

√

LpLs

, 0 ≤ kp/s ≤ 1 (4)

The undersea environment will modify the electrical char-

acteristics of the UWPT system, which will deteriorate the

efficiency of the system. Thus, a critical question is how to

optimize the coil design to improve efficiency? The following

section is to answer the question.

III. COIL ANALYSIS IN UNDERWATER ENVIRONMENT

In this section, we aim to understand the essential UWPT

parameters, such as the coils’ resistance, self-inductance, mu-

tual inductance and resonance frequency, which is critical for

optimized coil design and control purposes.

A. Resistance of a coil in seawater

The total resistance of a coil in air or seawater is the sum of

the coil’s DC resistance (Rdc) which depends on the conductor

size, the AC resistance (Rac) which is due to its skin depth,

and the radiation resistance (Rrad). Since the values of Rdc

and Rac depends on the coil configuration and the quality

factor of the wire, they remain almost the same either in

seawater or air. However, owing to the conductive nature of

seawater (σseawater ≈ 4S/m), electric currents are induced

by the magnetic field surrounding the coils. Hence Rrad could

differ significantly in seawater than in air [23], [24]. Here, we

examine the coil immersed in the seawater and compare it to

that in the air through the following formulas [25], [26]:

Rsearad = ωµa[

4

3(βa)2)− π

3(βa)3) +

2π

15(βa)5)− ...] (5)

Rairrad =

π

6

ω4µa4

c3(6)

where ω is the frequency in radians, µ is the permeability

of medium, a is the radius of the coil loop in meters,

β=(µωσ/2)1/2, and σ is the conductivity of the medium. As

can be seen Fig. 3:

• Rrad of the coil in the air is minuscule or almost

negligible;

• Rrad increases exponentially when the frequency is

greater than 200 kHz in seawater.

This means a UWPT transmitter coil should operate under

some threshold (e.g., 200 kHz). Otherwise, seawater begins to

have a detrimental effect and lead to more losses.

B. Inductance of a coil in seawater

The self-inductance (the ability of a device or component to

store energy in the form of a magnetic field) of a circular coil

can be calculated using (3). When the transmitter and receiver

coils are in close proximity, the current flowing through one

of these devices induced a voltage onto the other. This ability

to transfer energy inductively is measured by the mutual

inductance [27], [28], as expressed below:

Lm =µ0

4πNpNs

‹

e−γ|Rs−Rp|

|Rs −Rp|dlp·dls (7)

where γ ≈ √jωµ0σ, Np and Ns are the number of turns

of the primary and secondary coil, and the circular integrals

are over the path of a single turn of each coil. Equation (7)

applies to most coil structures except when the coil has very

few number of turns and the pitch is very large relative to

the wire diameter. Fig. 4 shows the magetic flux variation and

the influence of seawater on the characteristics of the mutual

inductance between the coils. Actually, the magnetic linkages

coupling the coils are significantly reduced as the distance





CL

1

/Receiver coil

Transmitter Coil

Seawater

Environment

Power source Primary side Secondary side DC-DC Converter

WEC (Docking Station) Ocean System (AUV)

Fig. 2. UWPT system configuration.

0 100 200 300 400 500 600

Frequency (kHz)

0

5

10

15

20

Re

sis

tan

ce

(Ω

)

Rrad

in Seawater

Rrad

in Air

Fig. 3. Simulation result showing comparison between radiation resistance inseawater and air (coil radius=10cm, number of turns=20, wire radius=0.4mm)

Seawater

Tx Coil(Transmitter)

Rx Coil(Receiver)

Fig. 4. Magnetic flux distribution in UWPT coil structure in seawater

between Tx and Rx increases, resulting in fast dropping mutual

inductance (see Fig. 5c).

Simulation results have been obtained on the UWPT system

with spiral-type coils, as shown in Figs. 5a–5d. It can be seen:

• The values of self-inductance of Tx and Rx and the

mutual inductance slightly increase as the radius of their

coil wires increases from 0.4 to 1-mm (see Figs. 5a–5c)

• The Rx self-inductance varies with distances between Tx

and Rx while the Tx self-inductance remains constant

(see Figs. 5a and 5b). Given identical Tx and Rx coil

radii, the peak value of the self-inductance of Rx can

become higher than that of Tx, resulting in compromised

power transfer efficiency (see Fig. 5d). The variation in

Rx coil is observed to be attributed to the rapid change in

distance when the coil is moved away from the Tx coil, in

a highly conductive salt water environment. We suspect

that the during this change the Rx coil behaves as if it had

a solid conductive core to some degree. However, it can

be noticed in Fig. 5b that the Rx inductance increase is

relatively small and begins to return to its original value

as the distance approaches 6 cm.

Consequently, to achieve maximum power transfer, the Tx

and Rx coil parameters cannot be identical. Rather, the radius

of Rx coil should be made smaller than that of Tx.

C. Coil Topology

It is interesting to determine a UWPT coil topology best

suited for integrating ocean distribution system (e.g., AUV).

In this paper, the characteristics of spiral-type coil (refer to

Fig. 4) and helix-type coil [29] in the undersea environment

are comparatively investigated. The design parameters such as

coil radius, wire diameter, pitch, and the number of turns of

both shapes are made identical for a fair comparison of the

effect of the coil shapes. Simulation results are illustrated in

Figs. 5e–5h. It can be seen:

• Given the change in distance, the coupling coefficient be-

tween the helix coils is much lower than that of the spiral

coils. Subsequently, the spiral-type coil is significantly

superior to helix-type coil in terms of much higher mutual

inductance and as a result higher coupling coefficient.

A similar study in [30] shows that when the distance

between the coil increases, the efficiency of the spiral

coil shape is better than that of helix coil. Therefore,

helix-type coil topology is hardly feasible for UWPT

application (see Figs. 5e and 5g).

• Increasing the number of turns in helix-type and spiral-

type coil topologies, surprisingly, does not improve the

coupling coefficient in either case. On the contrary, the

coupling coefficient decreases when increasing the num-

ber of turns of helix-type coil (see Figs. 5g and 5h).

In real-world situation the wire of the UWPT coil can be

protected from seawater using materials such as polyurethane

potting and encapsulating materials used on hydrophones.

These materials are required to resist the marine environment

over long periods of immersion. Based on the above analysis

of physical and topological characteristics, we can conclude

that the following rules should be considered for design and

operation of a UWPT:

1) Low frequency viability (operate at low frequencies);

2) Differentiation criterion (avoid identical Tx and Rx);

3) Close surface proximity (optimize coil topology to en-

hance coupling).





2 4 6 8 10Distance (cm)

1

1.5

2

2.5

3

Tx s

elf inducta

nce (

uH

)

0.4mm

0.6mm

0.8mm

1mm

(a)

2 4 6 8 10

Distance (cm)

1.5

2

2.5

3

Rx s

elf inducta

nce (

uH

)

0.4mm

0.6mm

0.8mm

1mm

(b)

2 4 6 8 10

Distance (cm)

0

200

400

600

800

Mutu

al in

ducta

nce (

nH

)

1mm

0.8mm

0.6mm

0.4mm

3.33 3.3301339.6

339.65

(c)

0 2 4 6 8 10

Distance (cm)

0

0.1

0.2

0.3

0.4

0.5C

ouplin

g C

oeffic

ient (k

)0.4mm

0.6mm

0.8mm

1mm

(d)

0 2 4 6 8 10

Distance (cm)

0

2

4

6

8

10

Mu

tua

l in

du

cta

nce

(µ

H) Helix coil

Spiral coil

(e)

0 2 4 6 8 10

Distance

0

0.2

0.4

0.6

0.8

Co

up

ling

co

eff

icie

nt

(k)

Helix coil

Spiral coil

(f)

0 2 4 6 8 10

Distance (cm)

0

0.1

0.2

0.3

0.4

Co

up

ling

co

eff

icie

nt

(k)

11 turns

12 turns

13 turns

14 turns

15 turns

(g)

0 2 4 6 8 10

Distance (cm)

0

0.2

0.4

0.6

0.8

Co

up

ling

co

eff

icie

nt

(k)

11 turns

12 turns

13 turns

14 turns

15 turns

(h)

Fig. 5. UWPT coil analysis based on simulation results (Base parameters:Number of turns=20, coil radius=10cm, wire radius=0.4mm; Subplots (a)-(d) obtained on spiral-type coils). (a) Tx self-inductance versus distance at adifferent wire radius. (b) Rx self inductance versus distance at a different wireradius. (c) Mutual inductance versus distance at a different wire radius. (d)Coupling coefficient versus distance at a different wire radius. (e) Comparisonof the mutual inductance between helix and spiral coil shape. (f) Comparisonof the coupling coefficient between helix and spiral coil shape. (g) Couplingcoefficient versus distance for helix-type coil (h) Coupling coefficient versusdistance for spiral-type coil

IV. OPTIMIZED COIL DESIGN PROCEDURE

Enabled by the findings in Section III, we present a system-

atic method for optimized coil design as depicted in Fig 6. The

operating frequency should first be determined according to

the power level of the UWPT system and frequency-dependent

circuit analysis such as that shown in Fig. 2. The design

procedure is presented as follows:

• Step 1: The UWPT system design constraints are imposed

based on application (e.g., AUV). The coil shape, relative

position of windings, the radius of the wire and number

of turns are determined, and the 3D model is constructed

Choose Tx and

Rx coil shape

(Helix/Spiral)

Set coil

dimension,

diameter, turns

Define region

(Sea/Fresh

water)

2. Apply initial value for distance between

Tx and Rx coil

3. Optimize coil parameters using Ansys

Magnetosatic solver

Resonance freq. close to

operating freq.?

5. Calculate and optimize compensating

capacitance

6. Perform parametric analysis at various

distances between Tx and Rx

4. Obtain optimized coil parameters

(mutual inductance, self-inductance, resistance)

7. Validate optimized coil design through

measurement of resonance freq.

8. Generate the dynamic flux and the

magnetic flux plot of the UWPT system

1. Define

the parameters of a practical UWPT system

No

Yes

Fig. 6. UWPT optimized coil design flowchart.

in finite element (FE) software. A seawater environment

is set up, and the associated Maxwell equations are

established.

• Step 2: Apply the initial value for distance between the

transmitter coil Tx and the reciever coil Rx.

• Step 3: The coil parameters are computed using a 3D FE

magnetostatic solver.

• Step 4: The values of self-inductances, mutual inductance

and the coupling coefficient between the coils are ob-

tained.

• Step 5: Compensating capacitors are chosen based on the

resonant frequency and the coil inductances using (3) and

(4).

• Step 6: Perform parametric sweep on the coils and obtain

optimized coil parameters at various distances.

• Step 7: Validate optimized coil design through measure-

ment of the resonant frequency using co-simulation with

ANSYS Simplorer. Confirm that the optimal frequency

is equal or very close to operating frequency.





• Step 8: The magnetic fields of the coils calculated based

on the optimized parameters of the coil from the magne-

tostatic analysis.

Since highly precise parameters are needed to get the

optimal solution, the above procedure heavily relies on the

transient analysis by a FE electromagnetic solver that re-

quires substantial computational resources. Therefore, high-

performance computing (HPC) facility is recommended to

solve the large-scale simulations with significantly reduced

design cycle. For instance, a simulation of a UWPT with 20-

turn coil on a PC could take more than 72 hours without

guaranteeing to find a solution. Whereas, an 8-core HPC is

able to reduce the simulation time to less than 12 hours and

achieve faster convergence.

The Table I in Section VI is an instance of an optimized

UWPT design using the above procedure.

V. MAXIMUM POWER EFFICIENCY TRACKING

A. Overview of Maximum Power Efficiency Tracking

The marine environment is highly uncertain and various

external forces will cause disturbances on the UWPT system.

The coupling coefficient kp/s that determines the power ef-

ficiency will fluctuate due to the motion between Tx and Rx

(e.g., wave energy converter station and AUV). The purpose of

this section is to devise a novel Maximum Power Efficiency

Tracking (MPET) that maintains the highest possible power

transfer efficiency. For a UWPT deployed in the marine envi-

ronment the power efficiency is dynamically changing with the

load conditions and the coupling coefficient between the coils.

There is a need to track the operating point corresponding to

the maximum power efficiency. For solar photovoltaic or wind

power applications Maximum Power Point Tracking (MPPT)

is a well-known concept. For UWPT applications, however,

maximum power efficiency is the most important property

to be maintained because it is critically important to reduce

power losses and preserve energy which is the most scarce

resource for undersea applications. Another major difference

from traditional MPPT is that our MPET does not need

any wireless communication between the transmitter and the

receiver which is highly desirable for smart ocean systems. In

fact, the k-nearest-neighbors-based machine learning approach

is used to estimate the coupling coefficient, making the MPET

attractive in practical applications where communication is not

viable, such as undersea environment.

First, equation (1) is re-examined to get the secondary

voltage:

Vs =(ω0Lm)RL

(RL +Rs)(RpRs + (ω0Lm)2)Vp (8)

Vs changes when the distance between Tx and Rx varies. Fig.

7 depicts the relationship between the Vs and power transfer

efficiency at different kp/s, under the assumption that the

amplitude of the primary voltage Vp and the internal resistance

of the primary side coil are constant. As can be seen, to achieve

maximum power efficiency at any specific kp/s, Vs should be

adjusted to an optimal value Vsmax. The reason why Vsmax

(derived below) leads to maximum power efficiency is because

101 102 103 104 105

Output voltage VS

(V)

0.2

0.4

0.6

0.8

1

Eff

icie

ncy

k20cm

=0.0069

k10cm

=0.093

k8cm

=0.197

k6cm

=0.248

k4cm

=0.383

k2cm

=0.592

MPET

VSmax

Fig. 7. Output voltage characteristics

Vsmaxcorrespond to a desirable RL satisfying the impedance

matching condition.

Vsmax=

√

Rs

Rp

ω0kp/s√

LpLs√

RpRs +√

RpRs + (ω0kp/s)2LpLs

Vp

(9)

Finding Vsmaxbecomes a significant challenge as it relies on

the real-time information of kp/s. One approach is to use in-

band wireless communication to transmit information between

Tx and Rx, in order to achieve impedance matching. Such

approach, however, is no longer viable in a marine environ-

ment since fast and cost-effective underwater communication

is currently unavailable [31]. To tackle this challenge, we

present a novel MPET method to force Vs → Vsmaxin real-

time using information from the Tx side only without relying

on wireless communication.

MPET controller

CalculateEquilibriumPoints

PIControllerCalculateOutputVoltageatMaxEff.

‐+

Pulse‐widthmodulator

_

+

‐

CL

Feedback

connection

EstimateCouplingCoeff. usingK‐NN

1

++

d D

Fig. 8. MPET control block

Fig. 8 summarizes our MPET approach. To be specific,

a k-nearest neighbors (kNN) is introduced to estimate kp/s





using only Rx information (Vs, Is). Subsequently, Vsmaxis

calculated using (9) and serves as the reference for feedback

control to track. As a salient feature, our MPET is an adaptive

tracker that updates the PI controller in real-time, and it

employs a DC-DC converter to achieve the task of changing

output voltage to desire voltage by adjust the duty ratio. This

feature makes the UWPT more resilient to the fast changing

kp/s.

B. Estimation of Coupling Coefficient

The Kirchhoff’s voltage law (KVL) equations for the UWPT

system in Fig. 2 (Tx and Rx side) can be derived as:

Vp = RpIp + ω0kp/sIp√

LpLs

Vs = ω0kp/s√

LpLsIs +RsIs(10)

Thus kp/s can be estimated by

kp/s =Vp ±

√

V 2p − 4RpIs(Vs +RpIs)

2Isω0

√

LpLs

(11)

kp/s is subject to uncertainties on the Tx and Rx sides.

Furthermore, it is infeasible to track both Tx and Rx states in

real-time without communication. To tackle the challenges, we

proposed a data-driven approach, kNN, for robust estimation

of kp/s under uncertainties, through local approximation using

recursive procedure. In particular, kp/s is learned from the

secondary voltages and currents as shown in algorithm 1.

Algorithm 1 Coupling coefficient estimation

1: Generate the dataset of pairs:

(x1, y1), (x2, y2), ..., (xN , yN ) where,

yi = Vp +√

V 2p − 4RpIs(Vs,i +RsIs,i )

xi = 2Is,i ω0

√

LpLs

2: Set a query point: xq

3: Compute the Euclidean distance from the query point to

the labeled dataset using

distance(xi, xq) =√

a1(xi − xq)2 + · · ·+ an(xn − xq)2

4: Sort the labeled samples in ascending order of distance

5: Find k closest xi in dataset (xNN1, ...xNNk) such that

for any xi not in nearest neighbor set distance(xi, xq) ≥distance(xNNK , xq)

6: Find a heuristic number k of nearest neighbors

7: Estimate the coupling coefficient which kp/s using knear-

est neighbors y = 1

k (yNN1 + · · ·+ yNNK)

Note that the real parts of the dominating poles in the

transfer functions from the primary and secondary voltages

to the secondary current are much faster than the fluctuation

frequency of coupling coefficient [32]. This means that the

transient response attenuate quickly and will hold true under

dynamics environment. Thus kp/s remains static in the UWPT.

This guarantees the validity and robustness of the proposed

kNN estimation method.

C. Modeling of the DC-DC converter

When reaching steady state, the DC-DC converter in Fig. 8

can be represented by an average state-space model as follows:

0 = AavX +BavU

Vdc = CavX(12)

where

Aav =

[

0 −DC

DL −Rb

L

]

,Bav =

[

1

C 00 − 1

L

]

,Cav =[

1 0]

X =

[

Vdc

IL

]

, U =

[

IdcVb

]

L, Rb, vdc and C are the inductance, the battery resistance,

the DC-link voltage, and the filter capacitor, respectively. The

battery voltage is Vb and the current flowing into the battery is

IL. The DC-DC converter states can then be found, as follows:

IL =IdcD

(13)

Vdc =VbD + IdcRb

D2(14)

where

D =VB ±

√

VB2 + 4VdcIdcRB

2Vdc(15)

Idc, IL, Vdc, and D are the steady-state values of idc(t), iL(t),

vdc(t), and ∆d, respectively.

During transient-state, to maintain a desired level of per-

formance of the MPET, discussed in the next section is a

PI controller that adjusts the error caused by the difference

between the output voltage Vdc and the reference voltage

Vdcmax, toward its original steady state values.

D. Controller Design

‐ +

_

α

β

++ +

+d D* DC‐DC

1++

Fig. 9. PI Controller Design

The control objective here is to adjust the output voltage

of the DC-DC buck converter towards the designated output

voltage on the load side, under all possible operating condi-

tions. The output voltage of DC-DC converter is a function of

the duty cycle ∆d. In order to regulated the output voltage,

the DC-DC converter should be controlled to regulate its duty

cycle.

We introduce an adaptive PI controller (see Fig. 9) that

adjust PI parameters in real-time [33]. This method is prefer-

able in that it achieves a desired level of performance of

the MPET control system when ∆d change with time. The

proportional constant (KP ) and integral constant (KI ) of the





TABLE IUWPT SYSTEM PARAMETERS

Parameters Tx side Rx side

Coil radius (cm) 6 5Number of turns 20 18Wire diameter (mm) 0.6 1Self-inductance (µH) 47 .8 20.3Parasitic resistance (ohms) 1.3 1.3Capacitor (nF) 53.1 38.5Operating frequency (kHz) 178 178AC voltage source (V) 150 –Switching frequency (KHz) – 100Load resistance (Ω) – 50

PI are adaptively adjusted by adjusting the values of α and

β, respectively. The transfer function of the PI controller is

described as follows:

GPI(s) = KP +KI

s(16)

α and β (whose values are KP and KI respectively during the

steady state) are adaptively varied as a function of error signal

verr value, so as to drive the steady state error to zero. As a

result, the dynamic output voltage deviation and the settling

time of the output voltage are reduced.

VI. SIMULATION RESULTS

The effectiveness of MPET has been verified on a UWPT

system with a primary voltage Vp of 150 V, an coil operating

frequency of 178 kHz and a switching frequency of 100 kHz

in its DC-DC converter. Three test cases are performed by

using MATLAB/Simulink and ANSYS Maxwell & Simplorer.

The first test case is to examine the resonant frequency at

which high power transfer efficiency of UWPT is expected.

The second test case is to validate the performance of kNN-

based coupling coefficient estimation. The third test case is to

verify the proposed MPET approach. The optimized UWPT

parameters used in the case studies are listed in Table I.

A. UWPT Resonance Frequency Analysis

To figure out the resonant frequency, the load of UWPT

system is varied from 10 Ω to 100 Ω with a step of 10 Ωwhile the distance between Tx and Rx coils is fixed at 1 cm

( i.e., kp/s fixed at 0.18).

As shown in Fig. 10, there exists an optimal resonance

frequency (i.e., 178 kHz) where a maximum efficiency is

consistently achieved even though the load varies between

10 Ω and 100 Ω. Therefore, the test UWPT system is to be

operated at 178 kHz in the following tests. It should be pointed

out, however, that the power transfer efficiency will vary

significantly as coupling coefficient between the transmitter

coil and the receiver coil varies (see Fig. 11). This means that

both the on-line coupling coefficient estimation and MPET are

indispensable to maintain high UWPT efficiency in the ever-

changing marine environment.

100 150 200 250 300

Frequency (KHz)

0

0.2

0.4

0.6

0.8

1

Effic

iency

RL=100Ω

RL=90Ω

RL=80Ω

RL=70Ω

RL=60Ω

RL=50Ω

RL=40Ω

RL=30Ω

RL=20Ω

RL=10Ω

Fig. 10. UWPT system efficiency (at kP/S = 0.18) as a function offrequency. Target resonance frequency set at 178 kHz for a wide range ofload resistance.

1

- 0 5J .

U

10-1

k p/s

,. -

50

L(µH)

100

(a)

0 20 40 60 80 100L

m(µH)

0

0.5

1

Eff

icie

ncy

10-2

10-1

100

kp/s

0

0.5

1

Eff

icie

ncy

(b)

Fig. 11. Simulation result showing the relationship between the couplingcoefficient kp/s, mutual inductance Lm, and efficiency at the same resonantfrequency f0 = 178kHz.





B. Coupling Coefficient Estimation

This case performs the kNN-based on-line estimation of

the coupling coefficient. For verification purpose, the exact

values of kp/s between the transmitter coil and the receiver

coil are analytically obtained from the simulated dataset of

primary and secondary circuit parameters. The kNN-based on-

line estimation is then performed under a specific condition

(e.g., a resonant frequency of 178 kHz and a load impedance

of 50 Ω). The comparison between the estimated kp/s values

and the exact values demonstrates the accuracy and efficiency

of the proposed estimation approach (see Fig12). In fact, it

takes less than 6.123s CPU time to obtain 1000 estimated

kp/s values with a maximum error of around 5%. It can be

seen that the maximum error occurs due to radiation loss when

the distance between Tx and Rx increases. This error can be

reduced by sampling more data at a longer period and filtering

measurement error. This proves the kNN-based approach is

well suited for the real-time MPET. More estimation results

-440

-2

300

kp/s

0

299.5

IS (A)

20

VS (V)

2

299298.5

0 298

Reference

Estimated kp/s

(a)

0 5 10 15 20 25 30 35 40

Is(A)

0

0.5

1

kp/s

coupling coefficient estimation

Estimated kp/s Reference

298 298.5 299 299.5 300

Vs(V)

0

0.5

1

kp/s

Estimated kp/s Reference

(b)

Fig. 12. Simulation result showing the comparison between reference

coupling coefficient (kp/s) and estimated coupling coefficient ( ˆkp/s) (a)Coupling coefficient estimation in 3D (b) Coupling coefficient estimation in2D

under different loading conditions have been obtained by using

impedance sweep, which have consistently verified the accu-

racy and effectiveness of the kNN-based estimation approach.

Those results are omitted due to the space limit.

C. UWPT Efficiency Maximization

0.5 1 1.5 2

Time (s)

0

20

40

60

Po

we

r (W

)

Pin

Pout

w/o MPET Pout

w/ MPET

kp/s8cm

kp/s4cm

kp/s10cm

(a)

0.5 1 1.5 2

Time (s)

0

0.5

1 E

ffic

iency

w/ MPET

w/o MPET

(b)

Fig. 13. Simulation result of MPET control for UWPT system. (a) UWPTpower output with and without MPET control (b) Maximum efficiency withand without MPET control.

The effectiveness of MPET is extensively evaluated on a

dynamic UWPT model subject to fast position changes, by

using ANSYS Maxwell & Simplorer and MATLAB/Simulink.

The former is employed to perform the transient analysis of

the UWPT, in order to obtain the values of the optimized coil

parameters. The latter run simulations with the Tustin solver

at a time-step of 10 µs to verify MPET.

In this test, the transmitter coil is fixed while the receiver

coil is originally placed at 1 cm and then quickly moved

further away at 4 cm, 8 cm and 10 cm. The output powers

and efficiencies of the UWPT system with and without MPET

are measured and illustrated in Fig.13. With MPET, when

the distance increases, a maximum power efficiency of 85%can be consistently tracked and a power transfer of 34W is

achieved. Without MPET, however, the output powers decline

and the efficiencies decreases drastically from 85% to 39%as the distance increases. It can also be seen that, when the

distance between the coils has a step (or near-step) change,

MPET is always able to quickly restore the maximum power

efficiency within 0.1 s, which validates the effectiveness and

robustness of the MPET.





0 0.5 1 1.5 2

Time (s)

(b)

0.8

0.9

1

Effic

iency

0 0.5 1 1.5 2

(a)

30

35

40P

ow

er

(W)

w/ noise w/o noise

Fig. 14. Simulation result showing the response of MPET when subject toAdditive white Gaussian noise (SNR=6db). (a) UWPT power output with andwithout noise (b) Maximum efficiency with and without noise

To further verify the robustness of MPET, the same test

is performed in a noisy environment when the output voltage

feedback signal and the PI controller are subject to an additive

white Gaussian noise with a signal to noise ratio of 6 db.

Fig.14 shows that MPET remains highly efficient and robust

under such noisy environment.

VII. EXPERIMENTAL VERIFICATION

To verify the analysis above, an experimental UWPT pro-

totype is implemented, as shown in Fig. 15. The experimental

setup consists of a power supply, transmitter and receiver coils,

micro-controller and power electronics converter, and a digital

oscilloscope. The target resonant frequency is set as 178KHz,

and the parameters used in this experiment system are set to

be the same as those in the simulations, except for the input

voltage which is set at 30V due to hardware limitation. All

submerged tests for the experiment are implemented in a 20-

gallon fish tank filled with seawater of 3.63% salt. Hence, these

solutions reasonably models a marine environment. Based on

the coil analysis in Section III, the coils are fabricated in a flat

spiral disk using 22 AWG wire, and their self-inductances are

measured using a complex impedance analyzer. As shown in

Fig. 16, the coils are placed onto a 3D printed disks to hold

them in place. The input and output cables are connected to

the Tx and Rx coil, respectively, and mounted on a test rig

that adjusts the distance between the coils.

On the transmitting side of the UWPT system, a DC source

is used to provide a constant voltage to an operational power

amplifier (APEX PA 94a) at 178KHz generated by a function

generator. The function generator used here could be replaced

by either a standalone function generator IC, or be created

using software on a micro-controller. The DC power supply

Fig. 15. Experimental setup of UWPT.

Fig. 16. UWPT transmitter and receiver test coil

of the power amplifier is set to its maximum range ±30V ,

creating an AC voltage of 30Vpp across the TX coil.

Meanwhile, on the receiving end of the UWPT system,

four SBR10U40CT diodes are used to build a standard full

bridge rectifier which converts the transferred AC voltage

signal to DC. A DC-DC buck converter described in Section

V subsequently used to step-down the voltage to a desired

voltage level. The control unit ATmega328p includes a 10-bit

analog-to-digital converter, which converter the voltage and

current to digitized data used to execute MPET.

Fig. 17 shows the measured results of the UWPT system;

when the Rx coil is placed at 1cm, 2cm, 3cm, and 4cm away

from the Tx coil. It can be seen that the voltage received

by the RX coil gradually reduces as the distance between

the transmitter and the receiver increases. Fig 17a -17d cor-

responds to power transfer efficiencies of 80%, 73%, 66%,

and 58%, respectively, through seawater. Fig. 18 gives the

measured power efficiency compared against the simulation

results, which shows close agreement between simulations and

experiments.

Fig. 19a shows the resonant frequency obtained by applying

the Fast Fourier Transform (FFT) on the raw data from the

oscilloscope. The result shows the power transfer efficiency is

maximized at the target resonant frequency. As the distance

increases from 1-10cm (target distance range of the UWPT)

the efficiency is still greater than 80%. However, when the

distance increases beyond the target range, the seawater begins

to have detrimental effect on the system and the efficiency

quickly decreases below 50% at the resonant frequency of





(a)

(b)

(c)

(d)

Fig. 17. Part of the experimental results. Transmitter and receiver voltagewaveform (a) at a distance of 1cm (b) at a distance of 2cm (c) at a distanceof 3cm (c) and at a distance of 4cm

178KHz. Fig. 19b shows the sensitivity of the UWPT system

when its deviate from the resonant frequency. Even though a

high efficiency of 80% is still feasible when the resonant fre-

quency deviate into a frequency range of [165KHz, 185KHz] a

variable capacitor is recommended to be used at the transmitter

0 2 4 6 8 10

Distance (cm)

0

0.5

1

Effic

iency

Experiment

Simulation

Fig. 18. Measured experimental result of the UWPT power transfer efficiencyat a distance between 1-10cm.

0 178 400 600 800 1000

Frequency (KHz)

0

0.2

0.4

0.6

0.8

1

Effic

iency (

%)

d=1cm

d=2cm

d=3cm

d=4cm

d=5cm

d=6cm

d=7cm

d=8cm

d=9cm

d=10cm

d=15cm

d=20cm

d=25cm

(a)

100 150 178 200 250 300

Frequency (KHz)

0

0.2

0.4

0.6

0.8

1

Eff

icie

ncy (

%)

178KHz

165KHz

200KHz

(b)

Fig. 19. Experimental results of UWPT resonance frequency (Target fre-quency is set at 178KHz). (a) Resonant frequency at a distance between 1-10cm versus efficiency (b) Sensitivity of the resonance frequency

side to bring the resonant frequency to its precise value as

in [34].

In Fig. 20a, when the distance between the Tx coil and

the Rx coil increases without control, the output voltage Vdc

after rectification drops significantly. In practice, as shown in

Fig. 20b, the buck converter can be controlled to regulate the





(a)

(b)

Fig. 20. Experimental results of the UWPT system. (a) Without controlwhen distance is adjusted from 1-10cm at unfixed interval (b) Controlledto a regulated output voltage of 12V.

output voltage at 12V in spite of the changes of the distance

between Tx and Rx.

VIII. CONCLUSION

This paper provides a deep understanding of transferring

power wirelessly in a dynamic undersea environment. Factors

that affect power transfer efficiency are analyzed in detail. A

systematic design approach is developed to optimize the coil

properties and thus improve the overall system efficiency. A

novel Maximum Power Efficiency Tracking (MPET) method

is then developed to estimate UWPT coupling coefficient in

real-time through machine learning and to effectively track

the maximum power efficiency (> 85%) when UWPT is

subject to the motion of the sea. Extensive simulation and

experimental tests have validated the effectiveness of the anal-

ysis, design and MPET approaches. The systematic methods

in this paper have opened a new door of opportunities for

smart ocean systems research. Our future research will be

focused on MPET for multiple source ocean energy systems,

new power electronic topologies that enables load variation

across broader range for better estimation purpose in MPET,

as well as advanced control strategies for MPET.

ACKNOWLEDGMENT

This material is based upon work supported by the National

Science Foundation under Grant No. 1647209 and Eversource

Energy Center under Grant No. 6200980.

The authors gratefully acknowledge the contributions of

Prof. Shengli Zhou for his valuable comments and helpful

suggestions. The authors would also like to thank Alex Sloss-

berg, Frank Ludorf, Walters Justin, and Kyle Buckley for their

assistance in setting up the hardware prototype of the UWPT

system.

REFERENCES

[1] Witricity. [Online]. Available: http://www.witricity.com/[2] Qualcomm/haloipt. [Online]. Available: http://www.qualcomm.com[3] J. M. Miller, O. C. Onar, and M. Chinthavali, “Primary-side power flow

control of wireless power transfer for electric vehicle charging,” IEEE

J. Emerg. Sel. Topics Power Electron., vol. 3, no. 1, pp. 147–162, Mar.2015.

[4] S. Y. R. Hui, W. Zhong, and C. K. Lee, “A critical review of recentprogress in mid-range wireless power transfer,” IEEE Trans. Power

Electrons., vol. 29, no. 9, pp. 4500–4511, Sept. 2014.[5] T. M. Hayslett, T. Orekan, and P. Zhang, “Underwater wireless power

transfer for ocean system applications,” in OCEANS 2016 MTS/IEEE

Monterey, Sept. 2016.[6] R. S. McEwen, B. W. Hobson, and L. McBride, “Docking control system

for a 54-cm-diameter (21-in) auv,” IEEE J. Ocean. Eng., vol. 33, no. 4,pp. 550–562, Oct. 2008.

[7] R. Stokey, B. Allen, and T. Austin, “Enabling technologies for remusdocking: an integral component of an autonomous ocean-samplingnetwork,” IEEE J. Ocean. Eng., vol. 26, no. 4, pp. 487–497, Oct. 2001.

[8] K. Teo, E. An, and P. J. Beaujean, “A robust fuzzy autonomous underwa-ter vehicle (auv) docking approach for unknown current disturbances,”IEEE J. Ocean. Eng., vol. 37, no. 2, pp. 143–155, Apr. 2012.

[9] W. Zhong and S. Y. R. Hui, “Maximum energy efficiency tracking forwireless power transfer systems,” IEEE Trans. Power Electrons., vol. 30,no. 7, pp. 4025–4034, Jul. 2015.

[10] A. P. Sample, D. Meyer, and J. R. Smith, “Analysis, experimental results,and range adaptation of magnetically coupled resonators for wirelesspower transfer,” IEEE Trans. Ind. Electron., vol. 58, no. 2, pp. 544–554, Feb. 2011.

[11] N. Y. Kim, K. Y. Kim, J. Choi, and C. W. Kim, “Adaptive frequency withpower-level tracking system for efficient magnetic resonance wirelesspower transfer,” Electron. Lett., vol. 48, no. 8, pp. 452–454, Apr. 2012.

[12] B. H. Waters, A. P. Sample, P. Bonde, and J. R. Smith, “Powering aventricular assist device (vad) with the free-range resonant electricalenergy delivery (free-d) system,” Proc. IEEE, vol. 100, no. 1, pp. 138–149, Jan. 2012.

[13] Z. Pantic, K. Lee, and S. M. Lukic, “Receivers for multifrequencywireless power transfer: Design for minimum interference,” IEEE J.

Emerg. Sel. Topics Power Electron., vol. 3, no. 1, pp. 234–241, Mar.2015.

[14] J. Park, Y. Tak, Y. Kim, Y. Kim, and S. Nam, “Investigation of adaptiveimpedance matching methods for near-field wireless power transfer,”IEEE Trans. Antennas Propag., vol. 59, no. 5, pp. 1769–1773, MayMay 2011.

[15] L. Huang, A. P. Hu, A. K. Swain, and Y. Su, “Z-impedance compen-sation for wireless power transfer based on electric field,” IEEE Trans.

Power Electron, vol. 31, no. 11, pp. 7556–7563, Nov. 2016.[16] T. C. Beh, T. Imura, M. Kato, and Y. Hori, “Basic study of improving

efficiency of wireless power transfer via magnetic resonance couplingbased on impedance matching,” in IEEE Int. Symp. Ind. Electron, 7 Jul.2010.

[17] F. Zhang, S. A. Hackworth, W. Fu, C. Li, Z. Mao, and M. Sun,“Relay effect of wireless power transfer using strongly coupled magneticresonances,” IEEE Trans. Magn., vol. 47, no. 5, pp. 1478–1481, MayMay 2011.

[18] D. Ahn and S. Hong, “A study on magnetic field repeater in wirelesspower transfer,” IEEE Trans. Ind. Electron., vol. 60, no. 1, pp. 360–371,Jan. 2013.

[19] M. J. Chabalko, J. Besnoff, and D. S. Ricketts, “Magnetic field en-hancement in wireless power with metamaterials and magnetic resonantcouplers,” IEEE Antennas Wireless Propag. Lett., vol. 15, pp. 452–455,Jul. 2015.

[20] E. S. Rodrguez, A. K. RamRakhyani, and D. Schurig, “Compact low-frequency metamaterial design for wireless power transfer efficiencyenhancement,” IEEE Trans. Microw. Theory Tech., vol. 64, no. 5, pp.1644–1654, May 2016.

[21] M. Ishihara, K. Umetani, H. Umegami, E.Hiraki, and M. Yamamoto,“Quasi-duality between ss and sp topologies of basic electric-fieldcoupling wireless power transfer system,” Electron. Lett., vol. 52, no. 25,pp. 2057–2059, Dec. 2016.





[22] T. Campi, S. Cruciani, F. Maradei, and M. Feliziani, “Near-field reduc-tion in a wireless power transfer system using lcc compensation,” IEEE

Trans. Electromagn. Compat., vol. 59, no. 2, pp. 686–694, Apr. 2017.[23] K. Iizuka, R. King, and C. Harrison, “Self- and mutual admittances of

two identical circular loop antennas in a conducting medium and in air,”IEEE Trans. Antennas Propag., vol. 14, no. 4, pp. 440–450, Jul. 1966.

[24] A. Jenkins, V. Bana, and G. Anderson, “Impedance of a coil in seawater,”in IEEE Antennas Propag. Soc. Int. Symp. (APSURSI), Jul. 2014.

[25] M. B. Kraichman, “Impedance of a circular loop antenna in a infniteconducting medium,” J. Res. Nat. Bur. of Std. Radio Propag., vol. 66D,no. 4, Jul. 1962.

[26] J. R. Wait, “Insulated loop antenna immersed in a conducting medium,”J. Res. Nat. Bur. of Std., vol. 59, no. 2, Aug. 1957.

[27] S. Babic, F. Sirois, C. Akyel, and C. Girardi, “Mutual inductancecalculation between circular filaments arbitrarily positioned in space:Alternative to grover’s formula,” IEEE Trans. Magn., vol. 46, no. 9, pp.3591–3600, Sep. 2010.

[28] C. Zhang, W. Zhong, X. Liu, and S. Y. R. Hui, “A fast method forgenerating time-varying magnetic field patterns of mid-range wirelesspower transfer systems,” IEEE Trans. Power Electrons., vol. 30, no. 3,pp. 1513–1520, Mar. 2015.

[29] P. Hadadtehrani, P. Kamalinejad, R. Molavi, and S. Mirabbasi, “On theuse of conical helix inductors in wireless power transfer systems,” inIEEE Canadian Conf. Elect. Comp. Eng. (CCECE), May 2016.

[30] X. Shi, C. Qi, M. Qu, S. Ye, G. Wang, L. Sun, and Z. Yu, “Effects ofcoil shapes on wireless power transfer via magnetic resonance coupling,”Journal of Electromagnetic Waves and Applications, vol. 28, no. 11, pp.1316–1324, 2014.

[31] Z. Zeng, S. Fu, H. Zhang, Y. Dong, and J. Cheng, “A survey ofunderwater optical wireless communications,” IEEE Commun. Surveys

Tuts., vol. 19, no. 1, pp. 204–238, Aug. Firstquarter 2017.[32] V. Jiwariyavej, T. Imura, and Y. Hori, “Coupling coefficients estimation

of wireless power transfer system via magnetic resonance coupling usinginformation from either side of the system,” IEEE J. Emerg. Sel. Topics

Power Electron., vol. 3, no. 1, pp. 191–200, Mar. 2015.[33] V. Arikatla, “Adaptive control methods for dc-dc switching power

converters,” Ph.D. dissertation, Univ. of Alabama, 2011.[34] J. Tian and A. P. Hui, “A dc-voltage-controlled variable capacitor for

stabilizing the zvs frequency of a resonant converter for wireless powertransfer,” IEEE Trans. Power Electrons., vol. 32, no. 3, pp. 2312–2318,Mar. 2017.

Taofeek Orekan (M’14) received the B.S. degreein electrical engineering from Kennesaw State Uni-versity, Atlanta, GA, USA, M.S. degree in electricalengineering from University of Connecticut, Storrs,CT, USA, and currently he is a Ph.D. candidate inelectrical engineering at University of Connecticut.His research interests include control of wirelesspower transfer systems, renewable energy, smartocean systems and smart grid.

Taofeek is a member of CIGRE, IEEE YoungProfessionals, and IEEE-HKN. He was a recipient

of the prestigious NSF GK-12 Fellowship award in 2014 and 2015.

Peng Zhang (M’07−SM’10) received the Ph.D.degree in electrical engineering from the Universityof British Columbia, Vancouver, BC, Canada, in2009. He is the Castleman Professor in EngineeringInnovation, and Associate Professor of ElectricalEngineering at the University of Connecticut, Storrs,USA. He was a System Planning Engineer at BCHydro and Power Authority, Vancouver. His researchinterests include software defined smart grid, micro-grids, smart and connected communities/cities, cybersecurity, and smart ocean systems. Dr. Zhang is a

Registered Professional Engineer in BC, Canada, and an individual memberof CIGRE.

Cyuansi Shih is a PhD candidate in MechanicalEngineering from University of Connecticut. He re-ceived his M.S. degree in Engineering Science fromNational Taiwan University. His research is in thearea of dynamics and control, adaptive cooperativecontrol and bio-mechanics.

Documents

IEEE JOURNAL OF EMERGING AND SELECTED TOPIC IN POWER